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A study of the ionospheric irregularities which cause spread-F echoes and scintillations of radio stars
Journal of Atmospheric andTerrestrial Physics. 1868:Vol.12,pp.34 to45. Per:anmn Press Ltd.,
Londm
A study of the ionospheric irregularities which cause spread-l: echoes and scintillations of radio stars B. H. BRIGGS Cavendish Laboratory, Cambridge (Received 13 August 1’357)
Abstract--A study is made of the correlation between the occurr’ence of spread-F echoes at Slough, Inverness and Oslo. It is concluded that the ionospheric imegularities which cause the spreading occur in patches which have dimensions of the order of CiOOkm in a NS direction, and considerably greater in the EW direction. There is an indication that these “bands” of irregularities may lie along lines of magnetic latitude, and that they tend to O~CUPin the same geographical position on successive nights. The correlation of the scintillations of the radio star in Cassiopeia with the occurrence of spread-P echoes at two places is investigated. The results am found to be consistent with the same picture of the spatial distribution of the irregularities. Some indirect arguments suggest that the irregularities causing the scintillations ape at heights near 300 km. 1.
IETRODUCTION
IN THIS paper we shall be concerned
with the phenomena of “spread-F” echoes, the scintillations of a radio star, and with the relation between them. We begin with a brief description of the two phenomena. Spread-F echoes are observed at certain times in vertical incidence soundings of The phenomenon is best seen on records of the virtual height as the ionosphere. a function of frequency (h’(f) records), as obtained at ionospheric observatories. There are several different kinds of spread-F, but the most common in medium latitudes takes the form of a thickening of the trace which becomes more marked #asthe critical frequency of the F region is approached (Fig. 1). The occurrence and nature of this phenomenon have been studied by various workers for different 1935; WELLS, 1954; R’EBER, 1964: 1956: stations (e.g. BOOKER and WELLS, WRIGHT, KOSTER and SKINNER, 1956). It is mainly a night-time phenomenon. Generally, spread-F echoes appear at sunset and the spreading increases throughout t,he night until layer sunrise, when there is a rapid decrease. In medium latitudes, the spreading is much more prevalent on winter nights than on summer nights. The spreading is generally believed to be due to the presence of pronounced irregularities in the ionization near the maximum of the F-region. Scintillations of a radio star take the form of irregular fluctuations in the strength and apparent position of the source. We shall here be concerned only with the amplitude variations of the radio waves as observed at a single point on the ground. These scintillations have been studied by many workers (e.g. RYLE and HEWISH, 1950; LITTLE and MAXWELL, 1951; HEWISH, 1952: HARTZ, 1955; WRIGHT, KOSTER and SKINNER, 1956; DAGG. 1957). At most places, the scintillations are found to be a night-time phenomenon, with a maximum of occurrence near midnight, and they are found to be correlated with spread-F echoes. It is therefore generally assumed that they are caused by the passage of the radio waves from the star through irregularities of ionization in the F region of the ionosphere, that these are the same as those which cause the spread-F echoes, and that they are present mainly by night. 34
A studyof the ionospheric irregularities whichcausespread-Pechoesand scintilltttions of radiostars
If observations are made when the star is at very low angles of elevation, a different type of scintillation is observed, which appears to be correlated with irregularities in the E region (BOLTON, SLEE and STAKLEY, 1953; WILD and ROBERTS, 1956). Also, for stations where there is considerable amoral activity the scintillations can occur at all times of day and vary as a function of sidereal rather than solar time (HARTZ, 1955). We shall not, however, be concerned with either of these effects in the present paper. We shall use scintillation data only for the source in Cassiopeia as observed at Cambridge, for which the scintillations are a night-time phenomenon, and are correlat,ed with the occurrence of spread-E’ echoes. In previous work on this subject, the occurrence of scintillations was compared with the occurrence of spread-F echoes at a single ionospheric station. %he region of the ionosphere effective for the production of scintillations was usually at a distance of several hundred kilometres from this station. The fact that a correlation was found between the two phenomena showed, therefore, that the irregularities occurred in patches of considerable horizontal extent. It was not possible, however, to determine the size of the patches. In the present paper we shall make use of observations at three ionospheric stations separated by about SO0 km. In this way it is possible to determine the approximate size and shape of the patches It is also possible by some indirect arguments to make deductions of irregularities. about thei.r height. In section 2 we begin by defining a “spread-F index” as a measure of the amount of spreading of the ionospheric echoes. We then study the correlation between the values of this index at the three ionospheric stations, and also the correlation between it’s mean value for one night and the next. Then in section 3 we define a “scintillation index” to represent the degree of variability of the waves from the radio star. We then study the correlation between the scintillation index and t’he spread-F index for two of the ionospheric stations. The significance of the results obtained is discussed in section 4. 2
A STUDY OF THE OCC~RREXCE OF SPREAD-F ECHOES AT THREE IONOSPHERIC STATION
(a) IleJinition of the “spread-P
index”
The three stations used for this study were Slough (52’N, low), Inverness (5i”N> 4OW) and Oslo (6O”N, 11”E). A.t these stations hourly h’(f) records are made as a routine. and the main parameters deduced from the records are published as monthly bulletins of ionospheric characteristics. For Slough and Inverness, t’he actual h’(f) records were available for study. but for Oslo only the mont’hly bulletins were available. A. different measure of spread-E’ was used in the two ca,se.s. When t’he h’(f) records were available, an index in the range O-3 was assigned to each hourly record according to the conventions illustrated in Fig. 1. An index of zero was given to records which showed no spreading, and a,n index of I to records which showed a very slight spreading near the critical frequency of the F region (Fig. l(a) and (b)). A.n index of 2 was given to records which showed 35
B. H. BRIGGS
considerable spreading but which still showed separated traces for the ordinary and extraordinary rays (Fig. I(c)). An index of 3 was given when the spreading was so great that the traces for the ordinary and extraordinary rays were completely joined up (Fig. l(d)). There were some unusual records which did not fit well into this classification. Some records showed “spurs” or diffuse echoes at a fairly constant height which extended above the normal critical frequency. These were usually associated with considerable spreading near the critical frequency, and were given an index of 3. Any spreading at levels well below the F region was ignored.
f
fo6
f
h'
Fig,
1. Diagrams which illustrate the development of spread-F echoes, and the index on a scaleO-3 used to measure the intensity of the phenomenon.
For Oslo, where only the monthly bulletins were available, use was made of the symbol “F” which is used in the bulletins to qualify the values of critical frequency when spreading is present. An index in the range O-3 was obtained from the bulletins as shown in Table 1. Table Typical Spread-F
published index
1
foFz j
0
1
1
I
2
i
3
It is believed that the indices obtained by the two methods measure essentially the same phenomenon, and are similar to the index used by other workers (e.g. WRIGHT, KOSTER and SKINNER, 1956). The index obtained from the records is, however, more reliable than that obtained from the bulletins. The present paper is based mainly on a detailed study of results for the following four months: September 1954, December 1954, March 1955, and June 1955. (b) Tlte correlation between the occurrence of spread-F echoes 012one night and the next Before we investigate the correlation between the values of the spread-F index a,t different stations, it is of interest to examine some features of the results for a single station. The figures obtained show at once the usual night-time increase. It can also be seen from the figures that if the index is high for any particular night, it tends to remain so for the whole of the night, or at any rate for a large part of it. Also, when the index is high, the spreading tends to start earlier and end later. 36
.% study of the ionospheric irregularities which cause spread-F echoes and scintillat,ions of radio stars
The question then arises: do nights of high or low spread-F occurrence occur in groups? To investigate this the mean value of the spread-F index for each night The series of figures obtained was subjected (1800-0600 G.M.T.) was evaluated. to an autocorrelation analysis for time shifts of 24 hr (i.e. one night) and 4S hr (i.e. t,wo nights). Th is was done separately for the four months, and the results for Slough and Inverness are given in Table 2.” The spread-F figures for Oslo were less reliable and mere not analysed in this way, but an inspect,ion of the figures suggest,s that t’he results would have been similar. Table Time
Slough
Inverness
2
shift,
24 hr
Sep. 1954 Dec. 1954 Mar. 1955 June 1955
+0.40 +0.20 +0.54
Sep. 1954 Dec. 1954 Mar. 1955 June 1955
+0.29 +O,OS +0.65 to.26
i & h :k
fO.30
y 0.06
Mean
48 hr
/
0 & 0.19 * 0.16 _L 0.18 5 0.13
+,.,‘:z::g
) ’
0.17 0.19 0.15 0.18
+0.05
(
* 0.19 0 * 0.19
to.13 +0.16 $0.57 -0.07
“* * +
0.19 0.18 0.16 0.19
+0.11
_c 0.07
I The res-ults show that for both stations there is a significant positive correlation between the mean spread-F index for one night and the next. The correlation coefficient between the mean spread-F index for nights separated by 48 hr is slightly positive, but is barely significant when the error is taken int’o account. Table
3
~ Time Slough
shift
June+Aug.
24 hr
I
+0.43
1950
48 hr
+ 0.08
+0.13
$I 0.10
72 hr
/
0 * 0.10
In view of the importance of this effect for any theory of the origin of spread-F echoes, a longer and independent series of results was analysed in a similar way. Records from Slough for the period 1 June 1950 to 31 August 1950 were used, and the results are shown in Table 3. _ * Throughout the present paper, the correlation coefficient p between n pairs of values of two variables z and y has been calculated from the equation czy P=
-&2 (4
The error o in ,I has been calculated
._ (E?!(cy) n (c2)2 n
Q2
3,”
I(
from the equation o = (1 -
37
n
!
$)/2/n
B. H. BRIGGS
These results agree quite well with the mean results in Table 2. We conclude that, at any one place, there is a tendency for nights of high spread-F index to occur in groups. (c) The correlation stations
between the occurrence
of spread-F
echoes at three ionospheric
In order to investigate the correlation between the occurrence of spread-J echoes at the three stations the figures for the mean spread-F index for the whole night at each station were used. The object now was to see whether the nights for which the spread-F index was above the monthly average for one station coincided with those for which it was above the average for the others. The correlation coefficient between the nightly figures was evaluated for each of the four months? and for the three pairs of stations Slough-Inverness, InvernessOslo, and Slough-Oslo. The results are shown in Table 4. It will be seen that the correlation between Slough and Inverness and between Slough and Oslo is zero within the limits of the error. For Inverness and Oslo, Table Correlation coefficient Slough-Inverness Sep. 1954
-608
*
Dec.
-0.22
+ 0.17
1954
March
1955
June 1955
0.19
+0.16
_c 0.19
+0.21
& 0.18
4
Correlation coefficient Inverness-Oslo
~
TO.58 * 0.13
(
$0.05
+ 0.19 ___-__
! Correlation coefficient I Slough-Oslo ~--;G4-&mGix-^
;
+0.19 _~0.15 1. L~L__
’
$0.35
+ 0.17
+0,12
7 0.18
,-
+0.43
*
0.17
+0.05
z 0.18
+0.35
*
0.08
I
Mean
I
to.02
I_ 0.09
~
/
4~0.10 -& 0.08
however, there is a significant positive correlation. As previously expla,ined. the index used for Oslo was of a different kind from t,hat used for Inverness. This difference could reduce the correlation between the two places, but it could not increase it. If the original records had been available from Oslo, so that the same kind of index could have been used, it is possible that the positive correlation would have been greater. It is of interest to consider the geographical positions of these stations; they are shown in Fig. 2. The distance between Slough and Inverness is 720 km and t,he line joining them lies approximately north-south. The distance between Inverness and Oslo is 920 km, and these stations have nearly the same geomagnet,ic latitude. (The dotted line marked “6O”W’ in Pi g. 2 is the parallel of 60”N magnetic latitude.) Their geographic latitudes dither by about) 3”. (The solid line marked :‘6T”C:” is the parallel of 57’N geographic lat’itude.) The significance of these results requires some discussion. In the first place, it should be pointed out that by using the mean value of the spread-F index for the -whole night we have elimina*ted the effect of the diurnal variation. If we had evaluated the correlation coefficient between the hourly figures, we would have 35
A study
of t’he ionospheric irregularities which cause spread-P
echoes and scintillations
of radio stars
found a positive correlation in all cases, because the diurnal variation is similar at the three stations. Secondly, it should be noted that a lack of correlation between two stations does not necessarily imply that if spread-F echoes are present at one station they are absent at the other. The correlation coefficient takes account only of deviations from the monthly mean value, and it is these deviations which are uncorrelated. We shall now attempt to int,erpret these results in terms of the spatial structure of the irregularities. If we had available a measure of the degree of irregularity at every point in the horizontal plane, we might expect to find that it would have the form of a two-dimensional function, which had a certain mean value together wit,h random variations around the mean. Our results place certain limits on the horizontal scale of this random pattern. The lack of correlation between Slough and Inverness shows that the scale in the north-south direction is less than 720 km. The positive correlation between Inverness and Oslo shows tha,t the scale measured in that direction is of the order of 920 km, and possibly much larger. We conclude that the pattern has a structure which is elongated in a roughly east-west direction. It is possible that the direction of elongation coincides with the parallels of geomagnetic latitude, though this cannot be decided with certainty from the present results. Such a pattern could be imagined to be built up by the superposition of “bands“ of irregularities, each band lying along a parallel of latitude. The fact that there is a correlation at any one station between the spread-F index for one night aud t,he next suggests that the structure of the pattern tends to recur, and the bands appear in similar geographical positions on successive nights. 3. A STVDY OF THE CORRELATION BETWEEN THE SCINTILLATIONS OF A RADIO STAR ABD THE SPREAD-F INDEX AT Two IONOSPHERIC STATIONS (a) Ikjnition
of the “scintillation
index”
RYLE and HEWISH (1950) defined in “index of fluctuation” of the waves from a radio star as the ratio of the mean deviation of the intensity to the mean intensity. For t#he present purposes it was sufficient to estimate the value of this quantity from an inspection of the records without actual measurements, and an index on a scale of O-5 was used. We shall call this quantity the “scintillation index.” The records used were for the source in Cassiopeia (23.01) as observed at Cambridge (52”N. 0”E). A. scintillation index was assigned to the records for each hour of the four months previously considered for which records were available. In general there were a,ppreciable scintillations only at night; the daytime records were in any case difficult to use owing to the presence of interference. A comparison of the scintillation results with the spread-F index at Slough and Inverness is made in the next two sections. The spread-P results for Oslo were not considered sufficiently reliable to justify their use in a detailed comparison. (b) The correlation between the scintillation index at Slough
index at Cambridge and the spread-F
A line from Cambridge to the source in Cassiopeia intersects the ionosphere in a point whose position depends on time as shown in Fig. 2. Three curves are shown 39
B. H. BRIGGS
for irregularities at three different heights. The figures on the curves are the time measured in hours after the upper culmination of the source (i.e. the hour angle). It will be seen that the effective region of the ionosphere for the production of scintillations is sometimes near Slough and sometimes hundreds of kilometres away. We have seen in section 2(c) that the spatial distribution of the irregularities is such that there is no correlation between points separated by distances of this order. We should, therefore, expect to find that near upper culmination the scintillation index would be correlated with the spread-F index at Slough. but at several hours away from upper culmination there should be no correlation.
Fig. 2. Map showing the three ionospheric observatories at Slough, Inverness and Oslo. The curves show the locus of the point of intersection with the ionosphere of a line from Cambridge to the source in Cassiopeia.
The correlation coefficients were calculated as follows. A particular hour was chosen and the series of scintillation figures for successive days of the month were compared with the corresponding spread-F figures. Each of the four months was analysed separately. By evaluating the correlation coefficient at a fixed time. the effect of the diurnal variation of the two quantities was removed. Any seasonal trend in the two quantities over one month was believed to be negligible. Thus the correlation coeficients refer only to the random variations of the two quantities, and are unaffected by diurnal or seasonal variations. A correlation coefficient is obtained in this way for each hour, and can be plotted as a function of local solar time or of the hour angle of the source. A given solar time corresponds to a different hour angle at different times of year. It was considered to be sufficiently accurate to use a mean value for the difference between solar time and hour angle for each month. 40
A study of the ionospheric
irregularities
which cause spread-F
echoes and scintillations
of radio stars
In Fig. 3 the correlation coefficient between the scintillation index observed at Cambridge and the spread-F index at Slough is plotted as a function of the hour angle of the source. A mean line has been drawn by eye through the points, which all lie within ho.2 of the line. As t,his is the error in the value of the correlation coefficients. the scatter around the mean line is no greater than would be expected
+o. .%+o p +o. z +o 8 +o 2
5 +o
5 0
-0
j
rk) 0 Hour5 after upper culmination
Fig.
3. The variation with hour angle of the correlation coefficient between index at Cambridge and the spread-F index at Slough. n December 1954 @ September 1954 q June 1955 @ March 1955
the scintillation
by chance. The result shows that the correlation is highest near upper culmination, and it is zero, or even slightly negative, near lower culmination. The line joining the effective region to Slough does not depart very much from the north-south direction. We can therefore investigate the size of the patches of irregularities in a north-south direction in the following way. From Fig. 2 we see that a given hour after upper culmination corresponds to a certain distance of the effective region from Slough. We can therefore replot the results of Fig. 3 to show
-“.10400
m Distance from Sloqh
Fig. 4. The correlation coefficient between the scintillation index and the spread-F index at Slough plotted as a function of the horizontal distance between the effective region of the ionosphere and the observing station at Slough.
how the correlation varies with the horizontal distance of the effective region from Slough. This is done in Fig. 4 for three different assumed heights of the irregularities. The correlation coefficient does not approach unity at zero distance as might at first sight be expected. The reasons for this may be any or all of the following:(i) inaccuracies in the scintillation and the spread-3 indices, which have been assigned to the records without quantitative measurements, (ii) variations in the heights of the irregularities which, if above the maximum of the F-region, may cause scintillation but no spread-F echoes, (iii) variations of the vertical thickness 4
41
B. H.
BRIGW
of the irregular region, which would affect t.he scintillation index more than the spread-P index. For these reasons, one would not expect to find perfect correlation In even if the two phenomena were measured at the same place in the ionosphere. spite of these difficulties, the curves of Fig. 4 serve to show the horizontal scale of the patches of irregularities. For example, if the height of 600 km is assumed, the correlation coefficient falls to one-half of its value at zero separation in a distance of about 800 km, a,nd if 400 km is assumed. in a distance of about 600 km. We can use the results of Fig. 4 to ma,ke some deductions about the height of Lhe irregularities. We have seen in section 2(c) that, there is zero correlation
Hours after upper culmination Fig.
5. The variation index
with hour angle of the correlation coefficient between at Cambridge and the spread-P index at Inverness. @ September 1954 3 June I!)55 0 March 1955
the scintillation
between the values of the spread-P index at points separated by 720 km in a north-south direction. This would be inconsistent with the curves of Fig. 4 unless the irregularities were situated at heights below about 300 km. We shall give other reasons later for rejecting a height much below 300 km, and we therefore adopt this figure as the most probable height. We then see from Fig. 4 that the correl&ion coefficient would drop to one-half of its value at zero separation in a distance of 450 km. We adopt this figure as the best estimate of the “size” of the patches in a north-south direction. (c) The correlation. between the scintillation i?ldex at inverness
index at Cambridge and the spwnd-P
In Fig. 5 the correlation coefficient between the scintillation index at Cambridge and the spread-F index at Inverness is plotted as a function of t’he hour angle. During December 1954, the correlation coefficient was found to be small at all times. It is suggested that this results from the fact that spread-F echoes were so prevalent at Inverness in this month that an indes of 3 was obtained for most of the night, so that the variations were not reproduced in t,he index. For this reason no points have been plotted in Fig. 3 for December.* It will be seen from Fig. 2 that the effective region of the ionosphere for the * It, will be noted also that in Table 4, December is the only month which shows zero corr&Gion between Inverness and Oslo. This is again believed to be due to the unreliability of the Inverness figures for this month.
42
d study of the ionospheric
irregularities
which cause spread.8
echoes and scintillatjions
of radio stars
production of scintillations is nearest to Inverness at about nine hours after upper culmination; the exact time of closest approach depends on the height assumed for the irregularities. The experimental curve of Fig. 5 shows an observed maximum of correlation near this time. The accuracy is not great enough to permit an exact determination of the time and hence of the height of the irregularities. We can, however. make some deductions about the height from the shape of the experimental curve. If the irregularities were at 600 km, the appropriate curve of Fig. 2 shows that the correlation should rise to a maximum seven hours after upper culmination, i.e. at the time of closest approach to Inverness. and should t’hen fall off again quite rapidly: owing to the rapid increase in the distance from Inverness. This is not oberved in the experimental curve. which is asymmetrical around t,he maximum, and maintains a positive correlation for many hours after the maximum. This is readily explained if the irregularities are near 300 km; for Fig. 2 then shows that after passing Inverness, the effective region moves approximately along a line of magnetic latitude. Similar arguments rule out a height much below 300 km. These conclusions are somewhat uncert,ain with the present data. owing to the la,rge scatter of the experimental points, but they could be made more precise if more results were analysed in a similar way. The method could be ext’ended by the use of data from more ionospheric stations. It is hoped that this type of analysis will be applied to the large amount of data on scintillations and spread-F echoes which will be accumulated during the International Geophysical Year. Curves similar to those of Fig. 4 cannot usefully be plotted for Inverness. This is because the line joining the effective region to Inverness varies .sreatly in direction: sometimes it is north-south and sometimes east-west. 4. DISCUSSIOX The results of section 2 and section 3 have shown that the irregularities which cause spread-F echoes and scintillations are not distributed uniformly in the horizontal plane, but occur in bands which lie along parallels of latitude. The dimensions of these bands are of the order of 450 km at right angles to the parallels of latitude? and considerably greater along the parallels of latitude. There appears to have been no previous work on the correlation of spread-F There have been simultaneous observations of echoes at’ separated stations. scintillations at two separated stations, and the results are consistent wit811t’he conclusions of the present paper. Thus SMITH: LITTLE and LOVELL (1950) compared the occurrence of scintillations at Jodrell Bank and Ca,mbridge; a separation The observations were made near of 210 km in a roughly north-south direction. upper culmination of the sources in Cygnus and Cassiopeia. It was found that the records were generally either steady at both sites or fluctuating at bot’h sites on a 10 per cent significant excepgiven night. There mere, however, approximately t’ions when the records were fluctuating at one place but not at the other. We concluded in section 3(b) that the correlation coefficient in a north-south line falls to one-half in a distance of 450 km. We should therefore expect a good but not perfect correlation at 210 km. which is consistent with the result,s obtained. Again F. G. Smith (private communication) compared t’he occurrence of scintillations at (Cambridge. England and Washingtonr D.C., U.S.A.. during six months of 1054 43
B. H. BRIGGS This result is again consistent with the sizes of the and found zero correlation. irregular regions deduced in the present paper. We will consider next the significance of the fact that the irregular regions tend to follow parallels of latitude. In connection with this fact we should also note that SPENCER (1955) concluded that the individual irregularities were elongated along the direction of the earth’s magnetic field. Both results indicate a marked magnetic control. They are also very similar to results of experiments on radio reflections from aurorae. The aurora1 echoes are found to be aspect sensitive in a way which could be explained if they were returned from ionized columns aligned along the direction of the earth’s field (BOOKER, GARTLEIN and NICHOLS, 1955). The reflecting regions also occur in bands along parallels of geomagnetic latitude, as. indeed. do some types of visible aurorae (BULLOUGH and KAISER, 1954, 1955; KAISER, 1957). Aspect-sensitive radio echoes have also been obtained from both the E and F regions at lower latitudes, where ordinary aurora1 echoes would not normally be expected (PETERSON, VILLARD, LEADABRAND and GALLAGHER, 1955). PETERSON ct al. described the echoes as rather like a weak southerly extension of the auroraltype echoes. It now seems likely that the irregularities which cause these echoes also cause spread-F echoes and scintillations. The similarity of all these phenomena has also been pointed out by KAISER (1956) and BOOKER (1956). If spread-F echoes are produced by irregularities aligned along the earth’s magnetic field, it seems probable tha.t the mean direction of arrival of the scattered waves would be at an angle to the vertical. Such directional effects would be worth looking for. The height of the irregularities deduced in section 3(b) and (c) was 300 km. HEWISH (1052) obta,ined a value of about 400 km from a diffraction argument. He also compared the scintillation result’s with the fading of waves reflected at vertical incidence, and found that on some occasions scintillations were present when the ionosphere behaved as a perfectly smooth reflector. From this he concluded that the irregularities were, on these occasions, above the level of reflection. This again led to a height of 400 km or above. It now seems likely that these observations could be explained differently. The effective region for the production of scintillations was at a considerable horizontal distance from the point of reflection. so that in view of the results of the present paper. a close correlation with the fading of the reflected wave would not be expected. The argument therefore loses its force. BOOKER (1956) rejected a height as great as 400 km on theoretical grounds: if the irregularities were due to turbulence. KAISER (1956) considered that the existence of stable irregularities with linear dimensions less than t’he mean free path was unlikely. With the dimensions given by SPENCER (1955) this sets an upper limit to the height at about 250 km. It should. however, be pointsed out that SPENCER’S figure of 3 km for the size of an individual irregularity relates only to the size across the direction of the earth’s magnetic field. Owing to the inhibiting effect of the field on diffusion, an irregularity could persist for some time even if it,s size measured across the field was smaller than the mean free path. We conclude that there is no valid objection, experimental or theoretical, to a height of 300 km. There is, of course, no reason why the irregula,rities should not be spread over a considerable range of heights centred on this value. 44
A study of the ionospheric irregularities
which cause spread-P
echoes and scintillations of radio stars
AcknouGdgements-This work has been carried out during the tenure of an Imperial Chemical Industries Fellowship. I am indebted to the Director of Radio Research, D.S.I.R., for making available the h’(f) records for Slough and Inverness. and to my wife for help with the calculation of the correlation coefficients. REFERENCES BOLTON J. G., SLEE 0. B. and STANLEY G. ,I. BOOKER H. G. BOOKER H. G., GARTLEIN C. W'. and
1953
Aust. J. Phys.
1956 1955
BOOKER H. (4. and WELLS &LLOIJGH K. and KAISER BULLOUGH K. and KAISER DAGG M. DAGG M. HARTZ '1‘.R. HEWISH A.
1938 1954 1955 1957 1957 1955 1952 1956 1957 1951 1955
Terr. Muag. Atmosph. Elect. 43, 249. J. Atmosph. Terr. I’hys. 5, 189. Ibid. 6, 198. J. Atmosph. Terr. I’h,ys. 10, 194. Ibid. 10, 204. Canad. J. Phys. 33,476. Proc. Roy. Sot. A 214, 494. Th,e Airglow and the Aurorae 11. 156 Pergamon Press, London. J. Geophys. Res. 62, 297. Phil. Msg. 42, 267. J. Geophys. Res. 60, 497.
1954 1956 1950 1950
Ibid. 59, 257. Ibid. 61, 157. Mon. Xot. R. Ast. r’ioc. Xature, Lond. 165, 422.
1955 1954 1956 1956
I’roc. Phys. SOC. B 68, 493. .I. Geophys. Res. 59, 273. .I. Atmosph. Terr. Phys. 8, 55. Ibid. 8, 240.
H. W. T. R. T. R.
KAISER 'r. It. LITTLE C. G. and MAXWELL A. PETERSON A. M., VILLARD 0. Cr. JR., LEADABRAND R. L. and GALLAGIIER P. B. REBER G. REBER (+. KYLE M. and HEWISH A. SMITH F. Cr.,LITTLE C. G. and LOVELL A. C. B. SPENCER M. WILU J. J'. and ROBERTS ~VRIGHT R. \I'.,KOSTER SE;INNER X'. .J.
J. A. J. R. and
45
6,434. 61,673.
110,381.
Londm
A study of the ionospheric irregularities which cause spread-l: echoes and scintillations of radio stars B. H. BRIGGS Cavendish Laboratory, Cambridge (Received 13 August 1’357)
Abstract--A study is made of the correlation between the occurr’ence of spread-F echoes at Slough, Inverness and Oslo. It is concluded that the ionospheric imegularities which cause the spreading occur in patches which have dimensions of the order of CiOOkm in a NS direction, and considerably greater in the EW direction. There is an indication that these “bands” of irregularities may lie along lines of magnetic latitude, and that they tend to O~CUPin the same geographical position on successive nights. The correlation of the scintillations of the radio star in Cassiopeia with the occurrence of spread-P echoes at two places is investigated. The results am found to be consistent with the same picture of the spatial distribution of the irregularities. Some indirect arguments suggest that the irregularities causing the scintillations ape at heights near 300 km. 1.
IETRODUCTION
IN THIS paper we shall be concerned
with the phenomena of “spread-F” echoes, the scintillations of a radio star, and with the relation between them. We begin with a brief description of the two phenomena. Spread-F echoes are observed at certain times in vertical incidence soundings of The phenomenon is best seen on records of the virtual height as the ionosphere. a function of frequency (h’(f) records), as obtained at ionospheric observatories. There are several different kinds of spread-F, but the most common in medium latitudes takes the form of a thickening of the trace which becomes more marked #asthe critical frequency of the F region is approached (Fig. 1). The occurrence and nature of this phenomenon have been studied by various workers for different 1935; WELLS, 1954; R’EBER, 1964: 1956: stations (e.g. BOOKER and WELLS, WRIGHT, KOSTER and SKINNER, 1956). It is mainly a night-time phenomenon. Generally, spread-F echoes appear at sunset and the spreading increases throughout t,he night until layer sunrise, when there is a rapid decrease. In medium latitudes, the spreading is much more prevalent on winter nights than on summer nights. The spreading is generally believed to be due to the presence of pronounced irregularities in the ionization near the maximum of the F-region. Scintillations of a radio star take the form of irregular fluctuations in the strength and apparent position of the source. We shall here be concerned only with the amplitude variations of the radio waves as observed at a single point on the ground. These scintillations have been studied by many workers (e.g. RYLE and HEWISH, 1950; LITTLE and MAXWELL, 1951; HEWISH, 1952: HARTZ, 1955; WRIGHT, KOSTER and SKINNER, 1956; DAGG. 1957). At most places, the scintillations are found to be a night-time phenomenon, with a maximum of occurrence near midnight, and they are found to be correlated with spread-F echoes. It is therefore generally assumed that they are caused by the passage of the radio waves from the star through irregularities of ionization in the F region of the ionosphere, that these are the same as those which cause the spread-F echoes, and that they are present mainly by night. 34
A studyof the ionospheric irregularities whichcausespread-Pechoesand scintilltttions of radiostars
If observations are made when the star is at very low angles of elevation, a different type of scintillation is observed, which appears to be correlated with irregularities in the E region (BOLTON, SLEE and STAKLEY, 1953; WILD and ROBERTS, 1956). Also, for stations where there is considerable amoral activity the scintillations can occur at all times of day and vary as a function of sidereal rather than solar time (HARTZ, 1955). We shall not, however, be concerned with either of these effects in the present paper. We shall use scintillation data only for the source in Cassiopeia as observed at Cambridge, for which the scintillations are a night-time phenomenon, and are correlat,ed with the occurrence of spread-E’ echoes. In previous work on this subject, the occurrence of scintillations was compared with the occurrence of spread-F echoes at a single ionospheric station. %he region of the ionosphere effective for the production of scintillations was usually at a distance of several hundred kilometres from this station. The fact that a correlation was found between the two phenomena showed, therefore, that the irregularities occurred in patches of considerable horizontal extent. It was not possible, however, to determine the size of the patches. In the present paper we shall make use of observations at three ionospheric stations separated by about SO0 km. In this way it is possible to determine the approximate size and shape of the patches It is also possible by some indirect arguments to make deductions of irregularities. about thei.r height. In section 2 we begin by defining a “spread-F index” as a measure of the amount of spreading of the ionospheric echoes. We then study the correlation between the values of this index at the three ionospheric stations, and also the correlation between it’s mean value for one night and the next. Then in section 3 we define a “scintillation index” to represent the degree of variability of the waves from the radio star. We then study the correlation between the scintillation index and t’he spread-F index for two of the ionospheric stations. The significance of the results obtained is discussed in section 4. 2
A STUDY OF THE OCC~RREXCE OF SPREAD-F ECHOES AT THREE IONOSPHERIC STATION
(a) IleJinition of the “spread-P
index”
The three stations used for this study were Slough (52’N, low), Inverness (5i”N> 4OW) and Oslo (6O”N, 11”E). A.t these stations hourly h’(f) records are made as a routine. and the main parameters deduced from the records are published as monthly bulletins of ionospheric characteristics. For Slough and Inverness, t’he actual h’(f) records were available for study. but for Oslo only the mont’hly bulletins were available. A. different measure of spread-E’ was used in the two ca,se.s. When t’he h’(f) records were available, an index in the range O-3 was assigned to each hourly record according to the conventions illustrated in Fig. 1. An index of zero was given to records which showed no spreading, and a,n index of I to records which showed a very slight spreading near the critical frequency of the F region (Fig. l(a) and (b)). A.n index of 2 was given to records which showed 35
B. H. BRIGGS
considerable spreading but which still showed separated traces for the ordinary and extraordinary rays (Fig. I(c)). An index of 3 was given when the spreading was so great that the traces for the ordinary and extraordinary rays were completely joined up (Fig. l(d)). There were some unusual records which did not fit well into this classification. Some records showed “spurs” or diffuse echoes at a fairly constant height which extended above the normal critical frequency. These were usually associated with considerable spreading near the critical frequency, and were given an index of 3. Any spreading at levels well below the F region was ignored.
f
fo6
f
h'
Fig,
1. Diagrams which illustrate the development of spread-F echoes, and the index on a scaleO-3 used to measure the intensity of the phenomenon.
For Oslo, where only the monthly bulletins were available, use was made of the symbol “F” which is used in the bulletins to qualify the values of critical frequency when spreading is present. An index in the range O-3 was obtained from the bulletins as shown in Table 1. Table Typical Spread-F
published index
1
foFz j
0
1
1
I
2
i
3
It is believed that the indices obtained by the two methods measure essentially the same phenomenon, and are similar to the index used by other workers (e.g. WRIGHT, KOSTER and SKINNER, 1956). The index obtained from the records is, however, more reliable than that obtained from the bulletins. The present paper is based mainly on a detailed study of results for the following four months: September 1954, December 1954, March 1955, and June 1955. (b) Tlte correlation between the occurrence of spread-F echoes 012one night and the next Before we investigate the correlation between the values of the spread-F index a,t different stations, it is of interest to examine some features of the results for a single station. The figures obtained show at once the usual night-time increase. It can also be seen from the figures that if the index is high for any particular night, it tends to remain so for the whole of the night, or at any rate for a large part of it. Also, when the index is high, the spreading tends to start earlier and end later. 36
.% study of the ionospheric irregularities which cause spread-F echoes and scintillat,ions of radio stars
The question then arises: do nights of high or low spread-F occurrence occur in groups? To investigate this the mean value of the spread-F index for each night The series of figures obtained was subjected (1800-0600 G.M.T.) was evaluated. to an autocorrelation analysis for time shifts of 24 hr (i.e. one night) and 4S hr (i.e. t,wo nights). Th is was done separately for the four months, and the results for Slough and Inverness are given in Table 2.” The spread-F figures for Oslo were less reliable and mere not analysed in this way, but an inspect,ion of the figures suggest,s that t’he results would have been similar. Table Time
Slough
Inverness
2
shift,
24 hr
Sep. 1954 Dec. 1954 Mar. 1955 June 1955
+0.40 +0.20 +0.54
Sep. 1954 Dec. 1954 Mar. 1955 June 1955
+0.29 +O,OS +0.65 to.26
i & h :k
fO.30
y 0.06
Mean
48 hr
/
0 & 0.19 * 0.16 _L 0.18 5 0.13
+,.,‘:z::g
) ’
0.17 0.19 0.15 0.18
+0.05
(
* 0.19 0 * 0.19
to.13 +0.16 $0.57 -0.07
“* * +
0.19 0.18 0.16 0.19
+0.11
_c 0.07
I The res-ults show that for both stations there is a significant positive correlation between the mean spread-F index for one night and the next. The correlation coefficient between the mean spread-F index for nights separated by 48 hr is slightly positive, but is barely significant when the error is taken int’o account. Table
3
~ Time Slough
shift
June+Aug.
24 hr
I
+0.43
1950
48 hr
+ 0.08
+0.13
$I 0.10
72 hr
/
0 * 0.10
In view of the importance of this effect for any theory of the origin of spread-F echoes, a longer and independent series of results was analysed in a similar way. Records from Slough for the period 1 June 1950 to 31 August 1950 were used, and the results are shown in Table 3. _ * Throughout the present paper, the correlation coefficient p between n pairs of values of two variables z and y has been calculated from the equation czy P=
-&2 (4
The error o in ,I has been calculated
._ (E?!(cy) n (c2)2 n
Q2
3,”
I(
from the equation o = (1 -
37
n
!
$)/2/n
B. H. BRIGGS
These results agree quite well with the mean results in Table 2. We conclude that, at any one place, there is a tendency for nights of high spread-F index to occur in groups. (c) The correlation stations
between the occurrence
of spread-F
echoes at three ionospheric
In order to investigate the correlation between the occurrence of spread-J echoes at the three stations the figures for the mean spread-F index for the whole night at each station were used. The object now was to see whether the nights for which the spread-F index was above the monthly average for one station coincided with those for which it was above the average for the others. The correlation coefficient between the nightly figures was evaluated for each of the four months? and for the three pairs of stations Slough-Inverness, InvernessOslo, and Slough-Oslo. The results are shown in Table 4. It will be seen that the correlation between Slough and Inverness and between Slough and Oslo is zero within the limits of the error. For Inverness and Oslo, Table Correlation coefficient Slough-Inverness Sep. 1954
-608
*
Dec.
-0.22
+ 0.17
1954
March
1955
June 1955
0.19
+0.16
_c 0.19
+0.21
& 0.18
4
Correlation coefficient Inverness-Oslo
~
TO.58 * 0.13
(
$0.05
+ 0.19 ___-__
! Correlation coefficient I Slough-Oslo ~--;G4-&mGix-^
;
+0.19 _~0.15 1. L~L__
’
$0.35
+ 0.17
+0,12
7 0.18
,-
+0.43
*
0.17
+0.05
z 0.18
+0.35
*
0.08
I
Mean
I
to.02
I_ 0.09
~
/
4~0.10 -& 0.08
however, there is a significant positive correlation. As previously expla,ined. the index used for Oslo was of a different kind from t,hat used for Inverness. This difference could reduce the correlation between the two places, but it could not increase it. If the original records had been available from Oslo, so that the same kind of index could have been used, it is possible that the positive correlation would have been greater. It is of interest to consider the geographical positions of these stations; they are shown in Fig. 2. The distance between Slough and Inverness is 720 km and t,he line joining them lies approximately north-south. The distance between Inverness and Oslo is 920 km, and these stations have nearly the same geomagnet,ic latitude. (The dotted line marked “6O”W’ in Pi g. 2 is the parallel of 60”N magnetic latitude.) Their geographic latitudes dither by about) 3”. (The solid line marked :‘6T”C:” is the parallel of 57’N geographic lat’itude.) The significance of these results requires some discussion. In the first place, it should be pointed out that by using the mean value of the spread-F index for the -whole night we have elimina*ted the effect of the diurnal variation. If we had evaluated the correlation coefficient between the hourly figures, we would have 35
A study
of t’he ionospheric irregularities which cause spread-P
echoes and scintillations
of radio stars
found a positive correlation in all cases, because the diurnal variation is similar at the three stations. Secondly, it should be noted that a lack of correlation between two stations does not necessarily imply that if spread-F echoes are present at one station they are absent at the other. The correlation coefficient takes account only of deviations from the monthly mean value, and it is these deviations which are uncorrelated. We shall now attempt to int,erpret these results in terms of the spatial structure of the irregularities. If we had available a measure of the degree of irregularity at every point in the horizontal plane, we might expect to find that it would have the form of a two-dimensional function, which had a certain mean value together wit,h random variations around the mean. Our results place certain limits on the horizontal scale of this random pattern. The lack of correlation between Slough and Inverness shows that the scale in the north-south direction is less than 720 km. The positive correlation between Inverness and Oslo shows tha,t the scale measured in that direction is of the order of 920 km, and possibly much larger. We conclude that the pattern has a structure which is elongated in a roughly east-west direction. It is possible that the direction of elongation coincides with the parallels of geomagnetic latitude, though this cannot be decided with certainty from the present results. Such a pattern could be imagined to be built up by the superposition of “bands“ of irregularities, each band lying along a parallel of latitude. The fact that there is a correlation at any one station between the spread-F index for one night aud t,he next suggests that the structure of the pattern tends to recur, and the bands appear in similar geographical positions on successive nights. 3. A STVDY OF THE CORRELATION BETWEEN THE SCINTILLATIONS OF A RADIO STAR ABD THE SPREAD-F INDEX AT Two IONOSPHERIC STATIONS (a) Ikjnition
of the “scintillation
index”
RYLE and HEWISH (1950) defined in “index of fluctuation” of the waves from a radio star as the ratio of the mean deviation of the intensity to the mean intensity. For t#he present purposes it was sufficient to estimate the value of this quantity from an inspection of the records without actual measurements, and an index on a scale of O-5 was used. We shall call this quantity the “scintillation index.” The records used were for the source in Cassiopeia (23.01) as observed at Cambridge (52”N. 0”E). A. scintillation index was assigned to the records for each hour of the four months previously considered for which records were available. In general there were a,ppreciable scintillations only at night; the daytime records were in any case difficult to use owing to the presence of interference. A comparison of the scintillation results with the spread-F index at Slough and Inverness is made in the next two sections. The spread-P results for Oslo were not considered sufficiently reliable to justify their use in a detailed comparison. (b) The correlation between the scintillation index at Slough
index at Cambridge and the spread-F
A line from Cambridge to the source in Cassiopeia intersects the ionosphere in a point whose position depends on time as shown in Fig. 2. Three curves are shown 39
B. H. BRIGGS
for irregularities at three different heights. The figures on the curves are the time measured in hours after the upper culmination of the source (i.e. the hour angle). It will be seen that the effective region of the ionosphere for the production of scintillations is sometimes near Slough and sometimes hundreds of kilometres away. We have seen in section 2(c) that the spatial distribution of the irregularities is such that there is no correlation between points separated by distances of this order. We should, therefore, expect to find that near upper culmination the scintillation index would be correlated with the spread-F index at Slough. but at several hours away from upper culmination there should be no correlation.
Fig. 2. Map showing the three ionospheric observatories at Slough, Inverness and Oslo. The curves show the locus of the point of intersection with the ionosphere of a line from Cambridge to the source in Cassiopeia.
The correlation coefficients were calculated as follows. A particular hour was chosen and the series of scintillation figures for successive days of the month were compared with the corresponding spread-F figures. Each of the four months was analysed separately. By evaluating the correlation coefficient at a fixed time. the effect of the diurnal variation of the two quantities was removed. Any seasonal trend in the two quantities over one month was believed to be negligible. Thus the correlation coeficients refer only to the random variations of the two quantities, and are unaffected by diurnal or seasonal variations. A correlation coefficient is obtained in this way for each hour, and can be plotted as a function of local solar time or of the hour angle of the source. A given solar time corresponds to a different hour angle at different times of year. It was considered to be sufficiently accurate to use a mean value for the difference between solar time and hour angle for each month. 40
A study of the ionospheric
irregularities
which cause spread-F
echoes and scintillations
of radio stars
In Fig. 3 the correlation coefficient between the scintillation index observed at Cambridge and the spread-F index at Slough is plotted as a function of the hour angle of the source. A mean line has been drawn by eye through the points, which all lie within ho.2 of the line. As t,his is the error in the value of the correlation coefficients. the scatter around the mean line is no greater than would be expected
+o. .%+o p +o. z +o 8 +o 2
5 +o
5 0
-0
j
rk) 0 Hour5 after upper culmination
Fig.
3. The variation with hour angle of the correlation coefficient between index at Cambridge and the spread-F index at Slough. n December 1954 @ September 1954 q June 1955 @ March 1955
the scintillation
by chance. The result shows that the correlation is highest near upper culmination, and it is zero, or even slightly negative, near lower culmination. The line joining the effective region to Slough does not depart very much from the north-south direction. We can therefore investigate the size of the patches of irregularities in a north-south direction in the following way. From Fig. 2 we see that a given hour after upper culmination corresponds to a certain distance of the effective region from Slough. We can therefore replot the results of Fig. 3 to show
-“.10400
m Distance from Sloqh
Fig. 4. The correlation coefficient between the scintillation index and the spread-F index at Slough plotted as a function of the horizontal distance between the effective region of the ionosphere and the observing station at Slough.
how the correlation varies with the horizontal distance of the effective region from Slough. This is done in Fig. 4 for three different assumed heights of the irregularities. The correlation coefficient does not approach unity at zero distance as might at first sight be expected. The reasons for this may be any or all of the following:(i) inaccuracies in the scintillation and the spread-3 indices, which have been assigned to the records without quantitative measurements, (ii) variations in the heights of the irregularities which, if above the maximum of the F-region, may cause scintillation but no spread-F echoes, (iii) variations of the vertical thickness 4
41
B. H.
BRIGW
of the irregular region, which would affect t.he scintillation index more than the spread-P index. For these reasons, one would not expect to find perfect correlation In even if the two phenomena were measured at the same place in the ionosphere. spite of these difficulties, the curves of Fig. 4 serve to show the horizontal scale of the patches of irregularities. For example, if the height of 600 km is assumed, the correlation coefficient falls to one-half of its value at zero separation in a distance of about 800 km, a,nd if 400 km is assumed. in a distance of about 600 km. We can use the results of Fig. 4 to ma,ke some deductions about the height of Lhe irregularities. We have seen in section 2(c) that, there is zero correlation
Hours after upper culmination Fig.
5. The variation index
with hour angle of the correlation coefficient between at Cambridge and the spread-P index at Inverness. @ September 1954 3 June I!)55 0 March 1955
the scintillation
between the values of the spread-P index at points separated by 720 km in a north-south direction. This would be inconsistent with the curves of Fig. 4 unless the irregularities were situated at heights below about 300 km. We shall give other reasons later for rejecting a height much below 300 km, and we therefore adopt this figure as the most probable height. We then see from Fig. 4 that the correl&ion coefficient would drop to one-half of its value at zero separation in a distance of 450 km. We adopt this figure as the best estimate of the “size” of the patches in a north-south direction. (c) The correlation. between the scintillation i?ldex at inverness
index at Cambridge and the spwnd-P
In Fig. 5 the correlation coefficient between the scintillation index at Cambridge and the spread-F index at Inverness is plotted as a function of t’he hour angle. During December 1954, the correlation coefficient was found to be small at all times. It is suggested that this results from the fact that spread-F echoes were so prevalent at Inverness in this month that an indes of 3 was obtained for most of the night, so that the variations were not reproduced in t,he index. For this reason no points have been plotted in Fig. 3 for December.* It will be seen from Fig. 2 that the effective region of the ionosphere for the * It, will be noted also that in Table 4, December is the only month which shows zero corr&Gion between Inverness and Oslo. This is again believed to be due to the unreliability of the Inverness figures for this month.
42
d study of the ionospheric
irregularities
which cause spread.8
echoes and scintillatjions
of radio stars
production of scintillations is nearest to Inverness at about nine hours after upper culmination; the exact time of closest approach depends on the height assumed for the irregularities. The experimental curve of Fig. 5 shows an observed maximum of correlation near this time. The accuracy is not great enough to permit an exact determination of the time and hence of the height of the irregularities. We can, however. make some deductions about the height from the shape of the experimental curve. If the irregularities were at 600 km, the appropriate curve of Fig. 2 shows that the correlation should rise to a maximum seven hours after upper culmination, i.e. at the time of closest approach to Inverness. and should t’hen fall off again quite rapidly: owing to the rapid increase in the distance from Inverness. This is not oberved in the experimental curve. which is asymmetrical around t,he maximum, and maintains a positive correlation for many hours after the maximum. This is readily explained if the irregularities are near 300 km; for Fig. 2 then shows that after passing Inverness, the effective region moves approximately along a line of magnetic latitude. Similar arguments rule out a height much below 300 km. These conclusions are somewhat uncert,ain with the present data. owing to the la,rge scatter of the experimental points, but they could be made more precise if more results were analysed in a similar way. The method could be ext’ended by the use of data from more ionospheric stations. It is hoped that this type of analysis will be applied to the large amount of data on scintillations and spread-F echoes which will be accumulated during the International Geophysical Year. Curves similar to those of Fig. 4 cannot usefully be plotted for Inverness. This is because the line joining the effective region to Inverness varies .sreatly in direction: sometimes it is north-south and sometimes east-west. 4. DISCUSSIOX The results of section 2 and section 3 have shown that the irregularities which cause spread-F echoes and scintillations are not distributed uniformly in the horizontal plane, but occur in bands which lie along parallels of latitude. The dimensions of these bands are of the order of 450 km at right angles to the parallels of latitude? and considerably greater along the parallels of latitude. There appears to have been no previous work on the correlation of spread-F There have been simultaneous observations of echoes at’ separated stations. scintillations at two separated stations, and the results are consistent wit811t’he conclusions of the present paper. Thus SMITH: LITTLE and LOVELL (1950) compared the occurrence of scintillations at Jodrell Bank and Ca,mbridge; a separation The observations were made near of 210 km in a roughly north-south direction. upper culmination of the sources in Cygnus and Cassiopeia. It was found that the records were generally either steady at both sites or fluctuating at bot’h sites on a 10 per cent significant excepgiven night. There mere, however, approximately t’ions when the records were fluctuating at one place but not at the other. We concluded in section 3(b) that the correlation coefficient in a north-south line falls to one-half in a distance of 450 km. We should therefore expect a good but not perfect correlation at 210 km. which is consistent with the result,s obtained. Again F. G. Smith (private communication) compared t’he occurrence of scintillations at (Cambridge. England and Washingtonr D.C., U.S.A.. during six months of 1054 43
B. H. BRIGGS This result is again consistent with the sizes of the and found zero correlation. irregular regions deduced in the present paper. We will consider next the significance of the fact that the irregular regions tend to follow parallels of latitude. In connection with this fact we should also note that SPENCER (1955) concluded that the individual irregularities were elongated along the direction of the earth’s magnetic field. Both results indicate a marked magnetic control. They are also very similar to results of experiments on radio reflections from aurorae. The aurora1 echoes are found to be aspect sensitive in a way which could be explained if they were returned from ionized columns aligned along the direction of the earth’s field (BOOKER, GARTLEIN and NICHOLS, 1955). The reflecting regions also occur in bands along parallels of geomagnetic latitude, as. indeed. do some types of visible aurorae (BULLOUGH and KAISER, 1954, 1955; KAISER, 1957). Aspect-sensitive radio echoes have also been obtained from both the E and F regions at lower latitudes, where ordinary aurora1 echoes would not normally be expected (PETERSON, VILLARD, LEADABRAND and GALLAGHER, 1955). PETERSON ct al. described the echoes as rather like a weak southerly extension of the auroraltype echoes. It now seems likely that the irregularities which cause these echoes also cause spread-F echoes and scintillations. The similarity of all these phenomena has also been pointed out by KAISER (1956) and BOOKER (1956). If spread-F echoes are produced by irregularities aligned along the earth’s magnetic field, it seems probable tha.t the mean direction of arrival of the scattered waves would be at an angle to the vertical. Such directional effects would be worth looking for. The height of the irregularities deduced in section 3(b) and (c) was 300 km. HEWISH (1052) obta,ined a value of about 400 km from a diffraction argument. He also compared the scintillation result’s with the fading of waves reflected at vertical incidence, and found that on some occasions scintillations were present when the ionosphere behaved as a perfectly smooth reflector. From this he concluded that the irregularities were, on these occasions, above the level of reflection. This again led to a height of 400 km or above. It now seems likely that these observations could be explained differently. The effective region for the production of scintillations was at a considerable horizontal distance from the point of reflection. so that in view of the results of the present paper. a close correlation with the fading of the reflected wave would not be expected. The argument therefore loses its force. BOOKER (1956) rejected a height as great as 400 km on theoretical grounds: if the irregularities were due to turbulence. KAISER (1956) considered that the existence of stable irregularities with linear dimensions less than t’he mean free path was unlikely. With the dimensions given by SPENCER (1955) this sets an upper limit to the height at about 250 km. It should. however, be pointsed out that SPENCER’S figure of 3 km for the size of an individual irregularity relates only to the size across the direction of the earth’s magnetic field. Owing to the inhibiting effect of the field on diffusion, an irregularity could persist for some time even if it,s size measured across the field was smaller than the mean free path. We conclude that there is no valid objection, experimental or theoretical, to a height of 300 km. There is, of course, no reason why the irregula,rities should not be spread over a considerable range of heights centred on this value. 44
A study of the ionospheric irregularities
which cause spread-P
echoes and scintillations of radio stars
AcknouGdgements-This work has been carried out during the tenure of an Imperial Chemical Industries Fellowship. I am indebted to the Director of Radio Research, D.S.I.R., for making available the h’(f) records for Slough and Inverness. and to my wife for help with the calculation of the correlation coefficients. REFERENCES BOLTON J. G., SLEE 0. B. and STANLEY G. ,I. BOOKER H. G. BOOKER H. G., GARTLEIN C. W'. and
1953
Aust. J. Phys.
1956 1955
BOOKER H. (4. and WELLS &LLOIJGH K. and KAISER BULLOUGH K. and KAISER DAGG M. DAGG M. HARTZ '1‘.R. HEWISH A.
1938 1954 1955 1957 1957 1955 1952 1956 1957 1951 1955
Terr. Muag. Atmosph. Elect. 43, 249. J. Atmosph. Terr. I’hys. 5, 189. Ibid. 6, 198. J. Atmosph. Terr. I’h,ys. 10, 194. Ibid. 10, 204. Canad. J. Phys. 33,476. Proc. Roy. Sot. A 214, 494. Th,e Airglow and the Aurorae 11. 156 Pergamon Press, London. J. Geophys. Res. 62, 297. Phil. Msg. 42, 267. J. Geophys. Res. 60, 497.
1954 1956 1950 1950
Ibid. 59, 257. Ibid. 61, 157. Mon. Xot. R. Ast. r’ioc. Xature, Lond. 165, 422.
1955 1954 1956 1956
I’roc. Phys. SOC. B 68, 493. .I. Geophys. Res. 59, 273. .I. Atmosph. Terr. Phys. 8, 55. Ibid. 8, 240.
H. W. T. R. T. R.
KAISER 'r. It. LITTLE C. G. and MAXWELL A. PETERSON A. M., VILLARD 0. Cr. JR., LEADABRAND R. L. and GALLAGIIER P. B. REBER G. REBER (+. KYLE M. and HEWISH A. SMITH F. Cr.,LITTLE C. G. and LOVELL A. C. B. SPENCER M. WILU J. J'. and ROBERTS ~VRIGHT R. \I'.,KOSTER SE;INNER X'. .J.
J. A. J. R. and
45
6,434. 61,673.
110,381.